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          java位运算
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        <h4 id="二进制"><a href="#二进制" class="headerlink" title="二进制"></a>二进制</h4><p>位：二进制位，简称 “位” 。是二进制计数系统中表示小于 2 的整数的符号，一般用 0 或者 1 表示，是具有相等概率的两种状态中的一种。二进制位的位数可表示一个机器字的字长，一个二进制位包含的信息量称为一比特（bit）。</p>
<p>一个栗子：</p>
<blockquote>
<p>举个栗子：<br> int占4个字节（byte）<br> 1byte = 8bit<br> 换算下来，一个int类型即占32bit<br> int i = 88; 这里的88为十进制，转换为二进制为：1011000，使用完整的32位表示即为：00000000 00000000 00000000 01011000</p>
</blockquote>
<span id="more"></span>
<h4 id="原码、反码和补码"><a href="#原码、反码和补码" class="headerlink" title="原码、反码和补码"></a>原码、反码和补码</h4><blockquote>
<p>在计算机内，有符号数有三种表示法：原码、反码以及补码。<br> 原码：就是二进制定点表示法，即最高位为符号位，“0”正负“1”，其余位表示数值的大小。<br> 反码：正数的反码与其原码相同；负数的反码是对正数逐位取反，符号位保持为1。<br> 补码：正数的补码与其原码相同；负数的补码是在其反码的末位加1。</p>
</blockquote>
<p>一个栗子：</p>
<blockquote>
<p>同样的，我们使用 “88” 举例说明原码、反码以及补码。<br> “88”的原码：00000000 00000000 00000000 01011000<br> “88”的反码：00000000 00000000 00000000 01011000<br> “88”的补码：00000000 00000000 00000000 01011000<br> 对于负数 “-88”，其原码、反码以及补码如下：<br> “-88”的原码：10000000 00000000 00000000 01011000<br> “-88”的反码：11111111 11111111 11111111 10100111<br> “-88”的补码：11111111 11111111 11111111 10101000</p>
</blockquote>
<h4 id="什么叫位运算"><a href="#什么叫位运算" class="headerlink" title="什么叫位运算"></a>什么叫位运算</h4><blockquote>
<p>程序中的所有数在计算机内存中都是以二进制的形式储存的。位运算就是直接对整数在内存中的二进制位进行操作。比如，and运算本来是一个逻辑运算符，但整数与整数之间也可以进行and运算。举个例子，6的二进制是110，11的二进制是1011，那么6 and 11的结果就是2，它是二进制对应位进行逻辑运算的结果（0表示False，1表示True，空位都当0处理）。</p>
</blockquote>
<p>下表列出了 <strong>位运算</strong> 的基本运算（A = 8，B = 9）</p>
<div class="table-container">
<table>
<thead>
<tr>
<th>操作符</th>
<th>描述</th>
<th>例子</th>
</tr>
</thead>
<tbody>
<tr>
<td>按位与&amp;</td>
<td>如果相对应位都是1，则结果为1，否则为0</td>
<td>A&amp;B=8，即1000</td>
</tr>
<tr>
<td>按位或\</td>
<td></td>
<td>如果相对应位都是0，则结果为0，否则为1</td>
<td>A</td>
<td>B=9，即1001</td>
</tr>
<tr>
<td>按位异或^</td>
<td>如果相对应位值相同，则结果为0，否则为1</td>
<td>A^B=1，即0001</td>
</tr>
<tr>
<td>按位取反~</td>
<td>按位取反运算符翻转操作数的每一位，即0变成1，1变成0</td>
<td>~A=7，即0111</td>
</tr>
<tr>
<td>左移 &lt;&lt;</td>
<td>按位左移运算符。左操作数按位左移右操作数指定的位数</td>
<td>A &lt;&lt; 2 = 32，即1000 00</td>
</tr>
<tr>
<td>右移 &gt;&gt;</td>
<td>按位右移运算符。左操作数按位右移右操作数指定的位数</td>
<td>A &gt;&gt; 2 = 2，即0010</td>
</tr>
</tbody>
</table>
</div>
<h4 id="位运算的常用小技巧"><a href="#位运算的常用小技巧" class="headerlink" title="位运算的常用小技巧"></a>位运算的常用小技巧</h4><h5 id="判断奇偶数"><a href="#判断奇偶数" class="headerlink" title="判断奇偶数"></a>判断奇偶数</h5><p><strong>只要根据最末位是 0 还是 1 来决定，为 0 就是偶数，为 1 就是奇数。</strong></p>
<p>因此可以用 <code>if((a &amp; 1) ==0)</code> 代替 <code>if(a % 2 == 0)</code> 来判断 a 是不是偶数。</p>
<p>一个栗子：</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">// 输出 0-100 之间的所有偶数</span></span><br><span class="line"><span class="keyword">for</span>(<span class="type">int</span> <span class="variable">i</span> <span class="operator">=</span> <span class="number">0</span>; i &lt; <span class="number">100</span>; i++) &#123;</span><br><span class="line">    <span class="keyword">if</span>((i &amp; <span class="number">1</span>) == <span class="number">0</span>) &#123;</span><br><span class="line">        System.out.println(i);</span><br><span class="line">	&#125;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>
<h5 id="交换两数"><a href="#交换两数" class="headerlink" title="交换两数"></a>交换两数</h5><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="type">int</span> <span class="variable">a</span> <span class="operator">=</span> <span class="number">1</span>, b = <span class="number">2</span>;</span><br><span class="line">a ^= b;</span><br><span class="line">b ^= a;</span><br><span class="line">a ^= b;</span><br><span class="line"></span><br><span class="line">System.out.println(<span class="string">&quot;a = &quot;</span> + a); <span class="comment">// a = 2</span></span><br><span class="line">System.out.println(<span class="string">&quot;b = &quot;</span> + b); <span class="comment">// b = 1</span></span><br></pre></td></tr></table></figure>
<h5 id="交换符号"><a href="#交换符号" class="headerlink" title="交换符号"></a>交换符号</h5><p>交换符号就是正数变成负数，负数变成正数。</p>
<p>因此变换符号只需要 <strong>执行取反操作 + 1 即可。</strong></p>
<p>一个栗子：</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="type">int</span> <span class="variable">a</span> <span class="operator">=</span> -<span class="number">15</span>, b = <span class="number">15</span>;</span><br><span class="line">System.out.println(<span class="string">&quot;a = &quot;</span> + (~a + <span class="number">1</span>)); <span class="comment">// a = 15</span></span><br><span class="line">System.out.println(<span class="string">&quot;b = &quot;</span> + (~b + <span class="number">1</span>)); <span class="comment">// b = -15</span></span><br></pre></td></tr></table></figure>
<h4 id="java-逻辑运算符"><a href="#java-逻辑运算符" class="headerlink" title="java 逻辑运算符"></a>java 逻辑运算符</h4><p>包含下面的6种：</p>
<ul>
<li><p><code>&amp;&amp;</code>: 短路与，其两边的表达式必须都是 true，才返回 true，否则返回 false。</p>
</li>
<li><p><code>&amp;</code>: 不短路与，其两边的表达式都会执行到</p>
</li>
<li><code>||</code>: 短路或，其两边的表达式只要有一个为 true，就返回 true，否则返回 false。</li>
<li><code>|</code>:  不短路或，其两边的表达式都会执行到</li>
<li><code>!</code>： 取相反的操作，若表达式为 true，返回 false，反之亦然。</li>
<li><code>^</code>: 当两边的表达式结果不一样时，返回 true， 一样时，返回 false。</li>
</ul>

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